Corresponding Author: S. Gao, Key Laboratory of Ocean Circulation and Waves, Institute of Oceanology, Chinese Academy of Sciences, 7 Nanhai Rd., Qingdao 266071, China. (firstname.lastname@example.org)
 The origin and pathway of Luzon Undercurrent (LUC) water are investigated using a simulated adjoint tracer, based on circulation estimates of a global general circulation model. The results demonstrate that most of the LUC water comes from the subtropical North Pacific, confirming the earlier hypothesis on its relation to the northward shift of the North Equatorial Current (NEC) bifurcation at subsurface. Of the total volume of initially tracer-tagged LUC water, approximately 41% is traced back to the winter mixed layer in the Kuroshio extension after 50 years of integration, coinciding with the formation of subtropical mode waters, while the rest is trapped in the northern subtropical gyre with its density >26.8 kg m−3, indicative of a significant South Pacific origin. As these waters move toward the western boundary, they get mixed and finally reach the density range of the LUC water. This result provides quantitative evidence for the dramatic impact of mixing on the route of subtropical water to becoming the LUC water.
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 There exists a complex current system in the low latitude western boundary of the North Pacific, where the North Equatorial Current (NEC) bifurcates as it approaches the east bank of the Philippines, splitting into the northward flowing Kuroshio and the southward flowing Mindanao Current (MC) [e.g., Nitani, 1972; Toole et al., 1990]. The NEC-MC-Kuroshio (NMK) current system is well known for its role in heat budget of the western Pacific warm pool [e.g.,Yuan and Hu, 1991; Clement et al., 2005], as well as for its direct involvement in the global ocean thermohaline circulation via the Indonesian and South China Sea throughflow [Gordon, 1986; Wang et al., 2011], both of which are important to the world's climate [Lukas et al., 1996].
 Subsurface currents were also observed underlying the NMK system. Among others, multiple northward velocity cores were found off Mindanao below about 500 m and named as the Mindanao Undercurrent (MUC) [Hu et al., 1991]. Based on the same data set, a southward flowing subsurface current was also seen underneath the Kuroshio east of Luzon [Hu and Cui, 1989; Lukas and Lindstrom, 1991], reflecting the northward shift of the NEC bifurcation with depth [Qu and Lukas, 2003]. This southward subsurface current, now known as the Luzon Undercurrent (LUC), starts to appear at depths below 500 m near 22°N, intensifies southward along the boundary, and eventually becomes part of the MC off Mindanao [Qu et al., 1997]. Both the MUC and LUC are believed to play a role in large-scale water exchanges of the global ocean [Fine et al., 1994; Bingham and Lukas, 1995].
 The present study focuses on the origin and pathway of the LUC in the North Pacific. Based on the mean meridional geostrophic velocity averaged within the 2°-longitude band east of Luzon,Qu and Lukas  suggested that the LUC is related to the northward shift of the NEC bifurcation at subsurface. This implies that a significant portion of the LUC water should come from the subtropical North Pacific, namely, the formation region of subtropical mode waters. But, the details have never been carefully examined.
 Having this in mind, the present study analyzes results from a simulated adjoint tracer [Fukumori et al., 2004]. Our specific goal is to examine where the LUC water originates. Another important issue to address is the effect of diapycnal mixing on the origin and pathway of the LUC water. The rest of the paper is organized as follows. A brief description of the model and method of analysis is presented in section 2. Characteristics of the LUC Water are described in section 3. Section 4 is devoted to identifying the origin and pathway of the LUC water. Results are summarized in section 5.
2. Model Description and Method of Analysis
2.1. Model Description
 Results from a model simulation of the consortium for Estimating the Circulation and Climate of the Ocean (ECCO) are utilized in this study. The ECCO model, based on the Massachusetts Institute of Technology general circulation model (MITGCM) [Marshall et al., 1997], is nearly global, extending from 80°S to 80°N. Horizontal grid spacing is 1° × 1° globally, except within 20° of the equator, where meridional grid spacing is gradually reduced to 0.3° within 10° of the equator. Vertical grid spacing is 10 m within 150 m of the surface, gradually increasing to 400 m toward the bottom of the domain. The K-profile parameterization (KPP) vertical mixing scheme ofLarge et al. is employed for realistic simulation of near-surface mixing processes. Convection is achieved by dramatically increasing the vertical mixing coefficient (from 5 × 10−6 to 0.1 m2 s−1) wherever the stratification is statically unstable. Mixing effects of mesoscale eddies are represented using the Redi  isoneutral mixing scheme and the Gent and McWilliams  (GM) parameterization. The GM–Redi coefficient is tapered as per Large et al. .
 The model is initially at rest with climatological temperature and salinity [Boyer and Levitus, 1997], and is spun up for 10-years, forced by time-mean seasonal wind stress and heat flux climatologies based on the Comprehensive Ocean–Atmosphere Data Set (COADS). Following the spin up, the model is forced from 1980 to the present by wind stress, heat flux, and evaporation minus precipitation estimates of the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis project. Sea surface temperature is relaxed to observed temperatures [Reynolds and Smith, 1994] with a spatially varying relaxation coefficient computed from the NCEP–NCAR product using the method employed by Barnier et al. . The equivalent of a freshwater flux is implemented by relaxing surface salinity to climatological values with a 60-day relaxation coefficient. Model velocity and mixing fields averaged in time with an interval of 10 days from 1980 to 2004 are employed in the present study.
 The ECCO model output has been analyzed by a number of studies. Among others, Fukumori et al.  investigated the origin and fate of the eastern equatorial Pacific surface waters (Nino 3 region). Qu et al.  recently examined the connection between the subtropics and tropics in the lower thermocline. Both studies suggest a reasonable representation of the ocean's circulation and water property distributions by the ECCO estimate.
 In the context of a general circulation model, the temporal evolution of a passive tracer is dictated by the same advection-diffusion equation as temperature and salinity, except for possible tracer sources and sinks
where c is the tracer concentration, uis the three-dimensional velocity vector, andκ = κKPP + κGM is the total mixing tensor, including the KPP vertical mixing tensor and the GM mesoscale eddies mixing tensor. Sources and sinks of the tracer as well as fluxes through boundaries are absent in this study. If a particular patch of water is uniformly initialized by a passive tracer, the subsequent movement of this tracer indicates the pathway of the initial patch of water.
 While passive tracers describe where the tracer-tagged water goes, the adjoint passive tracer can describe where the adjoint tracer-tagged water comes from. Tracing a given water mass backward in time can be achieved unambiguously within the context of the model simulation by a single integration of the adjoint of the passive tracerequation (1) [Vukićević and Hess, 2000]. Here, the adjoint of a passive tracer is defined as the sensitivity of a passive tracer at a given location (target) at a given time (terminal instant) to tracer perturbations at other locations at earlier instances. Therefore, such sensitivity indicates the relative importance of the past tracer concentrations to the target volume at the terminal instant. It will be nonzero if and only if water from such location can make its way to the target volume at the terminal instant. Thus, the value of this sensitivity relative to that of the target quantifies the fraction of water in the past that circulates from that location to the target location.
 Mathematically, an objective function J in discretized form is defined by the tracer concentration at particular location i at time t
where c(t) is a column vector of tracer concentration at all model grid points at time t. Vector ei is a zero vector except at the particular grid point of interest (i) where the element is 1. Using the chain rule, the sensitivity of J with respect to tracer concentrations at time step t-N can be written as
in which A is the model's state transition matrix. Equation (3) indicates that the sensitivity of the tracer at location i at time t to the tracer distribution at time t-N can be obtained by integrating the adjoint tracer equation (AT) backward in time with terminal condition ei. Thus the resulting value of the adjoint tracer at each grid point just corresponds to the fraction of that water mass that reaches point i at time t. Therefore, the adjoint sensitivity can be identified as describing where the target water mass (defined by J) was at the earlier instance (t-N). The reader is referred to Fukumori et al.  for a detailed deduction of the adjoint tracer equation.
 Note that considerable computational simplification is achieved in the numerical procedure by using precomputed 10-day running averaged circulation fields and mixing tensors. Differences between solutions with and without this approximation are proved to be negligible and 10-day sampling is sufficient in resolving the essential features of the water mass circulation [Fukumori et al., 2004]. In addition, the numerical scheme of the adjoint tracer equation conserves the adjoint tracer integral very well.
 As already noted by several earlier studies [Fukumori et al., 2004; Qu et al., 2009; Gao et al., 2011], the simulated adjoint tracer method provides an unambiguous means to identify water mass transport exactly as simulated by the model, whereas the traditional advective particle method does not account for mixing. Taking advantage of its unique backward tracing capability, the adjoint tracer method is employed in this study to identify the origin and pathway of the LUC water.
3. Characteristics of the LUC
 While the ECCO's resolution is relatively coarse, the general characteristics of the simulated circulation in the North Pacific look reasonable. Figure 1shows the long-term mean horizontal velocity field in December in the surface (0∼200 m) and subsurface (400 m∼800 m) layers. The results clearly demonstrate the northward shift of the NEC bifurcation with depth. In particular, the observed vertical structure of the LUC is well simulated by the model [Qu and Lukas, 2003]. Over the period of integration, the LUC can be seen most of the time, with its maximum velocity exceeding 5 cm. In most cases, the LUC strengthens in winter, when the NEC bifurcation reaches its northernmost position, and weakens in summer, in consistent with the southward shift of the NEC bifurcation. However, due to the vertical fluctuation of the Kuroshio and the westward propagation of mesoscale eddies, the long-term mean velocity of the LUC is relatively weak. As an example, meridional velocities at 16.2°N, 16.9°N, 17.6°N and 18.5°N in December 2004 are presented inFigure 2 to show the snapshot structure of the current. It can be seen that the LUC is located right beneath the Kuroshio at depths >400 m. As we progress northward, the core of the LUC gets deeper, and its maximum velocity decreases from ∼4 cm/s at 16.2°N to ∼1 cm/s at 18.5°N. This result is qualitatively consistent with those reported by earlier studies [Qu et al., 1998]. In a quantitative sense, however, the simulated LUC is somewhat weaker than the observations [e.g., Qu et al., 1998], presumably due to the coarse resolution of the model. Despite this quantitative discrepancy, the ECCO model's off-line circulation provides a unique means to identify the origin and pathway of the LUC water as discussed below.
4. Identifying the Origin of the LUC
 Recent studies suggest that stirring associated with time-dependent circulation can affect property distributions and pathways of a water mass [e.g.,Fukumori et al., 2004]. To identify the origin of the LUC, an adjoint tracer integration is conducted for the period between January 1980 and December 2004. The adjoint tracer is initialized uniformly to one unit value (in arbitrary tracer units per volume, ATU m−3) on 31 December 2004, for each grid point below 400 m in the 122°–128°E longitude band at 16.9°N. The meridional extension of initially released tracer is proportional to meridional velocity, so that the LUC velocity core has the largest contribution. No tracer is released in grid points whose meridional velocity is below 1.5 cm/s (Figure 3a). The tracer-tagged water falls between 26.6 and 27.2 kg m−3 in potential density, between 34.2 and 34.5 psu in salinity, and between 4° and 7°C in potential temperature (Figure 3b). The tracer is then traced backward in time, using velocity and mixing tensors of the simulation (section 2) averaged at 10-day intervals.
 Based on the fact that the subsurface water is formed by the process of subduction from the surface mixed layer, the origin of the LUC water is defined as where it is first traced back into the winter mixed layer in the integration. When any part of the water does so, we store its inventory and T–S properties and stop tracking it afterward. Computationally, the adjoint of passive tracer in the winter mixed layer is tabulated at the time point of winter and then reset to zero before the start of next year integration. Considering that water in the subtropical North Pacific may take up to 30 years or more to reach the LUC region, the 25 year circulation fields are used recurrently twice for a total integration of 50 years. With such a short time series, stirring associated with decadal variations cannot be easily identified. Nevertheless, the present analysis provides the first quantitative evidence for the origin of the LUC water.
4.1. The NEC Source
 Distribution of vertically integrated tracer content over the whole depth is presented as a function of years from its terminal time to illustrate the lateral circulation of the LUC water before reaching the western boundary of the North Pacific (Figure 4). Most (92%) of the tracer-tagged LUC water can be traced back to the eastern North Pacific in the first 5 years (Figures 4a–4e). This result confirms the earlier speculation on its NEC source [Qu and Lukas, 2003]. As a result of northward shift of the NEC bifurcation at subsurface, part of the NEC water turns to the south underneath the Kuroshio, and this forms the LUC along the western boundary. The velocity distributions of LUC (Figure 2) clearly demonstrate this depth dependence of the NEC bifurcation.
4.2. Subtropical Origin and Pathway
 After being traced back in the NEC, the mainstream of the tracer-tagged LUC water is seen all the way back to the subtropical North Pacific (Figure 4). It first appears in the formation region of Eastern Subtropical Mode Water (ESTMW) [e.g., Hautala and Roemmich, 1998] around year −15. But, none of it reaches the winter mixed layer there, since the density range of the LUC water is significantly heavier than the ESTMW. Then, it takes another 10–30 years to trace the water back to the Kuroshio extension region, where it eventually reaches the winter mixed layer (Figures 4h and 4i). This region is known as the formation region of Central Subtropical Mode Water (CMW) [cf., Talley, 1999; Hanawa and Talley, 2001], suggesting that the CMW is a major source of the LUC water. The high tracer concentration in the Kuroshio extension region corresponds well with a maximum in subduction rate [Qiu and Huang, 1995], presumably due to enhanced surface buoyancy flux stemming from intense evaporation and downward Ekman pumping there. Of the total volume of initially tracer-tagged LUC water, about 45% can be traced back into the winter mixed layer at year −50 (Figure 5), while the rest still remains in the subsurface and circulates within the North Pacific subtropical gyre. It is interesting that these source waters have different density ranges before they reach the western boundary, indicating that their pathways do not follow isopycnal surfaces. Diapycnal mixing is a major process responsible for these water transformations.
4.3. Effect of Diapycnal Mixing
 The adjoint tracer distributions against temperature and salinity further illustrate how the LUC water is transformed by diapycnal mixing (Figure 6). The initially tracer-tagged LUC water is confined betweenσθ = 26.6 and 27.2 kg m−3 at its terminal time (Figure 6a). As this water is traced backward in time, it gets mixed with water from both above and below, and is eventually split into two water masses. The lighter one has a density range between σθ = 25.4 and 26.6 kg m−3, corresponding to the CMW; the heavier one has a density σθ > 27.2 kg m−3, representing water of South Pacific origin. Of interest is that the two water masses have about the same salinity range in the eastern North Pacific, suggesting that the water transformations are largely due to temperature changes. As a consequence of diapycnal mixing, the waters' temperature and salinity changes are not density compensated. In general, water transformations are weak in the eastern North Pacific, and become most significant as the water masses approach the western boundary.
 In order to further evaluate the effect of mixing on the origin and pathway of the LUC water, a 50-year pure advection experiment is also conducted by using the model's velocity field only. In this experiment, a group of particles are uniformly initialized in the same location as the adjoint tracer (cf.Figure 3), with a depth interval of 50 m and a longitude interval of 1/2°. Then the particles are traced backward in time for 50 years. The resulting horizontal particle trajectories (Figure 7a) look similar to those in the adjoint tracer experiments. All particles come from the east, and 57% of them can be traced back to the winter mixed layer of the Kuroshio extension at year −50, with the rest recirculating in the deep subtropical gyre. The particles' movement against temperature and salinity (Figure 7b) indicates that they conserve their densities relatively well. Note that, since some of the eddy effects are already included in the velocity field, we still see significant diapycnal movements after the particles are subducted. In the intermediate and deeper layers, in particular, density changes are much smaller than those found in the adjoint tracer experiment. Unlike the adjoint tracer, no particles can get heavier than σθ = 27.2 kg m−3. This experiment confirms the dramatic impact of mixing on the origin of the LUC water.
5. Summary and Discussion
 The origin and pathway of the LUC water is investigated using a simulated adjoint tracer, based on circulation estimates of a global ocean general circulation model. In the absence of sources and sinks, the evolution of adjoint tracer content at a particular location relative to its terminal value provides useful insight into where the LUC water originates and how it reaches the western boundary. The adjoint tracer integration shows that most of the tracer-tagged LUC water can be traced back to the eastern subtropical gyre in the first 5 years of the integration. This result has confirmed the earlier speculation that the LUC is mainly supplied by the NEC, being closely related to the northward shift of the NEC bifurcation at subsurface [Qu and Lukas, 2003].
 Our results also indicate that the North Pacific subtropical gyre is the primary pathway of the LUC water. About 45% of the LUC water originates from the Kuroshio extension region, with the CMW being its major source. More than half of the LUC water can be traced back to the lower thermocline or upper intermediate layer of the subtropical gyre, where water has a density >27.2 kg m−3 and is believed to origin from the South Pacific. The current integration is not long enough to trace this water all the way back into its South Pacific origin.
Qu et al. in a recent study noticed that stirring associated with time variability and small-scale processes significantly affects property distributions and pathways of the 13°C Water in the eastern equatorial Pacific. Similar result is revealed for the LUC water. The adjoint tracer integration indicates that a significant portion of the CMW, after being subducted in the Kuroshio extension region, joins the thermocline circulation of the subtropical gyre. Meanwhile, denser water from below also moves toward the low latitudes of the North Pacific as part of the subtropical gyre. These waters gradually change their densities and eventually merge into the LUC water. Diapycnal mixing has dramatic impacts on the route of subtropical waters to becoming the LUC water. These impacts become most significant as the waters approach the lower latitude western boundary. The details require further investigation. In addition, the results presented here may be model-dependent. In other words, they may depend on the model's mixing parameters. Therefore, conducting a meaningful uncertainty analysis using different circulation fields and different mixing coefficients is an important topic for future study.
 This research was supported by Major Program of the National Natural Science Foundation of China through grant 40890151, the National Basic Research Program of China through grant 2012CB417402, and the National Science Foundation of China through grant 40876011. T. Qu was supported by NSF through grant OCE10-29704. The authors are grateful to I. Fukumori for long-term collaboration on the topic, to Z. Xing and I.-L. Tang for constant assistance in processing the model outputs and Y.-L. Chen and F. Wang for helpful discussions. SOEST contribution 8584 and IPRC contribution IPRC-866.